Recently much interest has arisen in the study of the time-fractional phase-field (TFPF) equations.
For instance, phase-field framework has been successfully employed to describe the evolution of structural damage and fatigue [1]}, in which the damage is described by a variable order time fractional
derivative.
In [2]} , the TFPF models account for the anomalously subdiffusive transport behavior in heterogeneous porous materials.
Liu et al. study the coarsening dynamics for the time-fractional Cahn-Hilliard (TFCH) model based on numerical observations in [2]}
, while Chen et al. consider the time-fractional molecular beam epitaxy model in [4]}.These problems are challenging due to the existence of both nonlocality and nonlinearity.
It is natural to extend the relevant discrete level intrinsic properties,
i.e., the maximum principle and energy stability to handle the
TFPF equations, e.g., [5]}, [6]}, [7]}.
